Download Math 107 Winter 2014 Quiz 1

Math 107
Winter 2014
Name
Student Number
1. (5 points) Sketch the following angles and convert to degrees
(a)
5
revolutions
6
degree measure =
(b)
7
revolution
4
degree measure =
2. (5 points) Sketch the following angles and convert to revolutions
(a) 45◦
radian measure =
(b) 390◦
radian measure =
Quiz 1
Math 107
Winter 2014
Quiz 2
Name
Student Number
1. (6 points) For each of the following angles give the quadrant in which the angle lies and give two coterminal
angles one positive and the other negative. (If no units are specified the angle is in radians.)
(a) 120◦
Quadrant:
Positive coterminal angle:
Negative coterminal angle:
(b)
7
π
4
Quadrant:
Positive coterminal angle:
Negative coterminal angle:
2. (2 points) Convert 120◦ to radian measure.
Radian measure:
3. (2points) Convert
Degree measure:
7
π to degree measure.
4
Math 107
Winter 2014
Quiz 3
Name
Student Number
As a bicycle moves along the ground its wheel, which has a diameter of 26 inches, rotates at 323 revolutions per
minute. What is the speed of the bicycle in miles per hour. (Note that the radius of the wheel is 13 inches and the
speed of the bicycle is the linear velocity v of a point on the outside of the tire.)
Math 107
Winter 2014
Name
Student Number
1. (5 points) If sin(θ) =
4
and θ is in quadrant II what is cos(θ)?
5
cos(θ) =
2. (5 points) Find all angles which satisfy the equation cos(θ) =
1
.
2
Quiz 4
Math 107
Winter 2014
Quiz 5
Name
Student Number
1. (4 points) If θ is an acute angle in a right triangle, θ is 20◦ and the side opposite θ has length 5 feet what is
the length of the hypotenuse of the triangle? (Give you answer to the nearest tenth of a foot.)
length of the hypotenuse
2. (6 points) sin(θ) =
csc(θ) =
tan(θ) =
4
and θ is in quadrant II. Find the exact values of the remaining circular functions of θ.
5
cos(θ) =
sec(θ) =
cot(θ) =
Math 107
Winter 2014
Quiz 6
Name
Student Number
1. (5 points) Find the exact value of each of the following or state that it is undefined. Your answers may involve
square roots. These should be done without a calculator.
(a) tan( π3 ) =
(b) sec( 7π
6 ) =
(c) cot(0) =
2. (5 points) Find all of the angles which satisfy the equation sec(θ) = 2.
Math 107
Winter 2014
Quiz 7
Name
Student Number
1. (5 points) Verify the identity
1 + tan(θ)
= csc(θ) + sec(θ). Show all steps.
sin(θ)
2. Find the exact value of sin(195◦ ). (This is a non-calculator problem. Your answer may have some square roots
in it.)
Math 107
Winter 2014
Quiz 8
Name
Student Number
1
2
The angle α is in Quadrant II and sin(α) = . The angle β is in Quadrant I and cos(β) = . Find the exact
3
3
value of cos(α + β).
Math 107
Winter 2014
Test 1
Name
Student Number
1. (20 points) Each row of the following table contains an angle given in either degrees, radians or revolutions.
Fill in the missing entries of the table. Give radian measures in terms of π.
Degree measure
45
Revolutions
Radian measure
◦
7
rev.
12
2π
3
360◦
17π
6
2. (16 points) For each of the following angles give the quadrant in which the angle lies and give two coterminal
angles (different from the given angle) one positive and the other negative. (If no units are specified the angle
is in radians.)
(a) 120◦
Quadrant:
Positive coterminal angle:
Negative coterminal angle:
(b)
−11π
3
Quadrant:
Positive coterminal angle:
Negative coterminal angle:
3. (18 points) A yo-yo which is 4 inches in diameter spins at a rate of 1500 revolutions per minute. How fast is a
point on the outer edge of the yo-yo moving in inches per minute? Round your answer to two decimal places.
Speed of the point:
4. (16 points) What is the speed of a point on the outer edge if the yo-yo from the previous problem in miles
per hour? Round to two decimal places.
Speed in miles per hour:
5. (18 points) If a point on the outer edge of the yo-yo is moving at a speed of 21362 inches per minute, what is
the angular velocity of the yo-yo in revolutions per minute? Round to two decimal places.
Angular Velocity:
6. (12 points) What are the following. Give exact values.
(a) cos(180◦ ) =
(b) sin( 3π
2 ) =
(c) cos( π6 ) =
(d) sin(45◦ ) =
Math 107
Winter 2014
Test 2
Name
Student Number
1. Find the exact values of
7π
(a) sin
=
4
(c) tan
7π
4
(b) cos
7π
4
=
=
2. Find all angles θ satisfying sin(θ) = − 12 .
Description of the angels
3. Find the measurements of the missing angles and the length of the missing sides. Give your answers to two
places right of the decimal.
A
c
θ
b
30
◦
16
θ=
C
c=
b=
4. The angle θ is in quadrant IV and sec(θ) = 45 . Find the exact values of the remaining circular functions.
cos(θ) =
cot(θ) =
sin(θ) =
tan(θ) =
csc(θ) =
5. Find all values of θ for which tan(θ) = 1.
Values of θ
6. A tower is standing vertically on level ground. It casts a shadow whose length is 525 feet. The angle of elevation
of the top of the tower from the tip of the shadow is 16◦ . How tall is the tower to the nearest foot?
Height of the tower